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Bakry–Émery curvature and model spaces in sub-Riemannian geometry

Barilari, D.
•
Rizzi, L.
2020
  • journal article

Periodico
MATHEMATISCHE ANNALEN
Abstract
We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry–Émery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound.
DOI
10.1007/s00208-020-01982-x
WOS
WOS:000521791500001
Archivio
http://hdl.handle.net/20.500.11767/128688
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85082931715
https://arxiv.org/abs/1906.08307
Diritti
metadata only access
Soggetti
  • 53C17

  • 49J15

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